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   <div id="projectbrief">c++ math library</div>
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<div class="title">quaternion.cpp</div>  </div>
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<a href="quaternion_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160; </div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;</div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="__gbmath_8h.html" title="MAIN INCLUDE HEADER. ">_gbmath.h</a>&quot;</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;</div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;</div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="keyword">namespace </span>gbmath</div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;{</div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;</div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno"><a class="code" href="classgbmath_1_1_quaternion.html#a08abd49fa41bda4037c9230a78e62724">   10</a></span>&#160;<a class="code" href="classgbmath_1_1_quaternion.html" title="standard quaternion. ">Quaternion</a>&amp;  <a class="code" href="classgbmath_1_1_quaternion.html#a08abd49fa41bda4037c9230a78e62724" title="set as rotation from matrix ">Quaternion::setRotationMatrix</a>(<span class="keyword">const</span>  <a class="code" href="structgbmath_1_1mat44.html" title="matrix 4x4. ">mat44</a>&amp; m)</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;{</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;</div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;    <span class="keywordtype">float</span> fTrace = m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[0][0] + m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[1][1] + m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[2][2];</div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;    <span class="keywordtype">float</span> fRoot;</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;    <span class="keywordflow">if</span> (fTrace &gt; 0.0)</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;    {</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;        fRoot =  sqrt(fTrace + 1.0f);</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;         <a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a> = 0.5f * fRoot;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;        fRoot = 0.5f / fRoot;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;         <a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> = (m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[1][2] - m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[2][1]) * fRoot;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;         <a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> = (m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[2][0] - m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[0][2]) * fRoot;</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;         <a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> = (m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[0][1] - m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[1][0]) * fRoot;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    }</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    {</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;        <span class="keyword">static</span> <span class="keywordtype">size_t</span> s_iNext[3] = { 1, 2, 0 };</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;        <span class="keywordtype">size_t</span> i = 0;</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        <span class="keywordflow">if</span> (m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[1][1] &gt; m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[0][0] ) i = 1;</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;        <span class="keywordflow">if</span> (m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[2][2] &gt; m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[i][i] ) i = 2;</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;        <span class="keywordtype">size_t</span> j = s_iNext[i];</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        <span class="keywordtype">size_t</span> k = s_iNext[j];</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;        fRoot =  sqrt(m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[i][i] - m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[j][j] - m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[k][k] + 1.0f);</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        <a class="code" href="classgbmath_1_1_quaternion.html#a1e0bfdecbadcffcf920226f49c95dabb">floats</a>[i] = 0.5f * fRoot;</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;        fRoot = 0.5f / fRoot;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a> = (m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[j][k] - m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[k][j]) * fRoot;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        <a class="code" href="classgbmath_1_1_quaternion.html#a1e0bfdecbadcffcf920226f49c95dabb">floats</a>[j] = (m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[i][j] + m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[j][i]) * fRoot;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        <a class="code" href="classgbmath_1_1_quaternion.html#a1e0bfdecbadcffcf920226f49c95dabb">floats</a>[k] = (m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[i][k] + m.<a class="code" href="structgbmath_1_1mat44.html#abfc90602ae12e59095d384cd61ce970a">floats</a>[k][i]) * fRoot;</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    }</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;   <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;}</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"><a class="code" href="classgbmath_1_1_quaternion.html#a9fa6f57f2e920e75bdfc800b4b94ede7">   52</a></span>&#160;<a class="code" href="classgbmath_1_1_quaternion.html" title="standard quaternion. ">Quaternion</a> <a class="code" href="classgbmath_1_1_quaternion.html#a9fa6f57f2e920e75bdfc800b4b94ede7">Quaternion::slerp</a>( <span class="keyword">const</span> <a class="code" href="classgbmath_1_1_quaternion.html" title="standard quaternion. ">Quaternion</a> &amp;q1, <span class="keywordtype">float</span> t )</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;{</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <a class="code" href="classgbmath_1_1_quaternion.html" title="standard quaternion. ">Quaternion</a> res;</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordtype">float</span> k0,k1,cosomega = this-&gt;<a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> * q1.<a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> + this-&gt;<a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> * q1.<a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> + this-&gt;<a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> * q1.<a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> + this-&gt;<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a> * q1.<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a>;</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <a class="code" href="classgbmath_1_1_quaternion.html" title="standard quaternion. ">Quaternion</a> q;</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <span class="keywordflow">if</span>(cosomega &lt; 0.0)</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    {</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;        cosomega = -cosomega;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        q.<a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> = -q1.<a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a>;</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;        q.<a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> = -q1.<a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a>;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        q.<a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> = -q1.<a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a>;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        q.<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a> = -q1.<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a>;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    }</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    {</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        q.<a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> = q1.<a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a>;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        q.<a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> = q1.<a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a>;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;        q.<a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> = q1.<a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a>;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;        q.<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a> = q1.<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a>;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    }</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    <span class="keywordflow">if</span>(1.0 - cosomega &gt; 1e-6)</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    {</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        <span class="keywordtype">float</span> omega = acos(cosomega);</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        <span class="keywordtype">float</span> sinomega = sin(omega);</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        k0 = sin((1.0f - t) * omega) / sinomega;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        k1 = sin(t * omega) / sinomega;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    }</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    {</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        k0 = 1.0f - t;</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;        k1 = t;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    }</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    res.<a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> = this-&gt;<a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> * k0 + q.<a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> * k1;</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    res.<a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> = this-&gt;<a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> * k0 + q.<a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> * k1;</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    res.<a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> = this-&gt;<a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> * k0 + q.<a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> * k1;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    res.<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a> = this-&gt;<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a> * k0 + q.<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a> * k1;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;}</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;</div>
<div class="line"><a name="l00095"></a><span class="lineno"><a class="code" href="classgbmath_1_1_quaternion.html#a4b17875d52a506da9c927c50b2a4b82c">   95</a></span>&#160;<a class="code" href="classgbmath_1_1_quaternion.html" title="standard quaternion. ">Quaternion</a> <a class="code" href="classgbmath_1_1_quaternion.html#a4b17875d52a506da9c927c50b2a4b82c" title="return exponentiation ">Quaternion::pow</a>(<span class="keyword">const</span> <a class="code" href="classgbmath_1_1_quaternion.html" title="standard quaternion. ">Quaternion</a> &amp;q, <span class="keywordtype">float</span> exponent)<span class="keyword"> const</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    <span class="keywordflow">if</span> (fabs(q.<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a>) &gt; .9999f) </div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    {</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;        <span class="keywordflow">return</span> q;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    }</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    <span class="comment">// Extract the half angle alpha (alpha = theta/2)</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    <span class="keywordtype">float</span>   alpha = acos(q.<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a>);</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    <span class="comment">// Compute new alpha value</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <span class="keywordtype">float</span>   newAlpha = alpha * exponent;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <span class="comment">// Compute new w value</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    <a class="code" href="classgbmath_1_1_quaternion.html" title="standard quaternion. ">Quaternion</a> result;</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    result.<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a> = cos(newAlpha);</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    <span class="comment">// Compute new xyz values</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <span class="keywordtype">float</span>   mult = sin(newAlpha) / sin(alpha);</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    result.<a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> = q.<a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> * mult;</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    result.<a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> = q.<a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> * mult;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    result.<a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> = q.<a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> * mult;</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    <span class="comment">// Return it</span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;}</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;</div>
<div class="line"><a name="l00129"></a><span class="lineno"><a class="code" href="classgbmath_1_1_quaternion.html#af6ff0daa4332218515e5ebc99a0d759f">  129</a></span>&#160;<a class="code" href="structgbmath_1_1vec3.html" title="3d-base vector. Corrected by operators epislon ">vec3</a> <a class="code" href="classgbmath_1_1_quaternion.html#af6ff0daa4332218515e5ebc99a0d759f">Quaternion::getRotationAxis</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    <span class="comment">// Compute sin^2(theta/2).  Remember that w = cos(theta/2),</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    <span class="comment">// and sin^2(x) + cos^2(x) = 1</span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    <span class="keywordtype">float</span> sinThetaOver2Sq = 1.0f - <a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a>*<a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a>;</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    <span class="comment">// Protect against numerical imprecision</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <span class="keywordflow">if</span> (sinThetaOver2Sq &lt;= 0.0f) </div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    {</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;        <span class="comment">// Identity quaternion, or numerical imprecision.  Just</span></div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;        <span class="comment">// return any valid vector, since it doesn&#39;t matter</span></div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;        <span class="keywordflow">return</span>  <a class="code" href="structgbmath_1_1vec3.html" title="3d-base vector. Corrected by operators epislon ">vec3</a>(1.0f, 0.0f, 0.0f);</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    }</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <span class="comment">// Compute 1 / sin(theta/2)</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keywordtype">float</span>   oneOverSinThetaOver2 = 1.0f / sqrt(sinThetaOver2Sq);</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    <span class="comment">// Return axis of rotation</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    <span class="keywordflow">return</span>  <a class="code" href="structgbmath_1_1vec3.html" title="3d-base vector. Corrected by operators epislon ">vec3</a> (</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        <a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> * oneOverSinThetaOver2,</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;        <a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> * oneOverSinThetaOver2,</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;        <a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> * oneOverSinThetaOver2</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;        );</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;}</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;</div>
<div class="line"><a name="l00162"></a><span class="lineno"><a class="code" href="classgbmath_1_1_quaternion.html#ae655dc102b620ebe8673bad796e6d382">  162</a></span>&#160;<a class="code" href="classgbmath_1_1_quaternion.html" title="standard quaternion. ">Quaternion</a>&amp;  <a class="code" href="classgbmath_1_1_quaternion.html#ae655dc102b620ebe8673bad796e6d382">Quaternion::setRotationAxis</a>(<span class="keyword">const</span>  <a class="code" href="structgbmath_1_1vec3.html" title="3d-base vector. Corrected by operators epislon ">vec3</a> &amp;axis, <span class="keywordtype">float</span> theta)</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;{</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;    <span class="comment">// The axis of rotation must be normalized</span></div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;    <span class="comment">// a ssert( fabs(vectorMag(axis) - 1.0f) &lt; 0.01f );</span></div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;    <span class="comment">// Compute the half angle and its sin</span></div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> thetaOver2 = theta*0.5f;</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> sinThetaOver2 = sin(thetaOver2);</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    <span class="comment">// Set the values</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <a class="code" href="classgbmath_1_1_quaternion.html#a7fe1a860e7668f2176c694372224c492">w</a> = cos(thetaOver2);</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    <a class="code" href="classgbmath_1_1_quaternion.html#a3882c651300845816e1217cba2603365">x</a> = axis.<a class="code" href="structgbmath_1_1vec3.html#a5fb2cf8734338da1ad7b4251a3bde292">x</a> * sinThetaOver2;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    <a class="code" href="classgbmath_1_1_quaternion.html#a840d387bebcaf33ee8120e27da850b50">y</a> = axis.<a class="code" href="structgbmath_1_1vec3.html#aa096d36a3c46c4224f0195f70eb580ec">y</a> * sinThetaOver2;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <a class="code" href="classgbmath_1_1_quaternion.html#a59b779f21113c09d454efcec2091c8ba">z</a> = axis.<a class="code" href="structgbmath_1_1vec3.html#a546e6c38e7c49102f064d130ed3475ee">z</a> * sinThetaOver2;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;}</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;</div>
<div class="line"><a name="l00183"></a><span class="lineno"><a class="code" href="classgbmath_1_1_quaternion.html#ad72d193610738b2a50edfcc13b45e8a2">  183</a></span>&#160;<span class="keyword">inline</span> <a class="code" href="structgbmath_1_1axies__angle.html" title="The axis of rotation and angle. ">axies_angle</a> <a class="code" href="classgbmath_1_1_quaternion.html#ad72d193610738b2a50edfcc13b45e8a2">Quaternion::getRotationAxiesAngle</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;    <a class="code" href="structgbmath_1_1axies__angle.html" title="The axis of rotation and angle. ">axies_angle</a> res;</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;    res.<a class="code" href="structgbmath_1_1axies__angle.html#a2fb6ad4c87854ac8c8aa27885705b9db" title="rotation angle ">angle</a> = <a class="code" href="classgbmath_1_1_quaternion.html#ac83b75488f1951f411f5aa7f0acc6ca2">getRotationAngle</a>();</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    res.<a class="code" href="structgbmath_1_1axies__angle.html#a319f2ec9b8869ef2b875d064794d0359" title="axis of rotation (should be normalized) ">axies</a> = <a class="code" href="classgbmath_1_1_quaternion.html#af6ff0daa4332218515e5ebc99a0d759f">getRotationAxis</a>();</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;    <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;}</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;</div>
<div class="line"><a name="l00192"></a><span class="lineno"><a class="code" href="classgbmath_1_1_quaternion.html#a80dccf15808d9a43985d3aa9fdadf672">  192</a></span>&#160;<a class="code" href="structgbmath_1_1axies__angle.html" title="The axis of rotation and angle. ">axies_angle</a> <a class="code" href="classgbmath_1_1_quaternion.html#a80dccf15808d9a43985d3aa9fdadf672">Quaternion::toAxiesAngle</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="classgbmath_1_1_quaternion.html#ad72d193610738b2a50edfcc13b45e8a2">getRotationAxiesAngle</a>();</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;}</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;</div>
<div class="line"><a name="l00198"></a><span class="lineno"><a class="code" href="classgbmath_1_1_quaternion.html#a725cba36f6123017327b7a8269456adc">  198</a></span>&#160;<a class="code" href="classgbmath_1_1_quaternion.html" title="standard quaternion. ">Quaternion</a>&amp;  <a class="code" href="classgbmath_1_1_quaternion.html#ae655dc102b620ebe8673bad796e6d382">Quaternion::setRotationAxis</a>(<span class="keyword">const</span> <a class="code" href="structgbmath_1_1axies__angle.html" title="The axis of rotation and angle. ">axies_angle</a>&amp; aa)</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;{</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="classgbmath_1_1_quaternion.html#ae655dc102b620ebe8673bad796e6d382">setRotationAxis</a>( aa.<a class="code" href="structgbmath_1_1axies__angle.html#a319f2ec9b8869ef2b875d064794d0359" title="axis of rotation (should be normalized) ">axies</a> , aa.<a class="code" href="structgbmath_1_1axies__angle.html#a2fb6ad4c87854ac8c8aa27885705b9db" title="rotation angle ">angle</a> );</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;}</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;</div>
<div class="line"><a name="l00204"></a><span class="lineno"><a class="code" href="classgbmath_1_1_quaternion.html#a451eb63222c75d8afb85210153356c51">  204</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classgbmath_1_1_quaternion.html#a451eb63222c75d8afb85210153356c51" title="Construct turning the corners Eller. ">Quaternion::setRotationEulersAngles</a>(<span class="keyword">const</span> <a class="code" href="classgbmath_1_1euler__angles.html" title="Ehler angles. Angles of rotation along all three axes. ">euler_angles</a>&amp; ea)</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;{</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    <a class="code" href="classgbmath_1_1_quaternion.html#ae3547e45e6da7cbe5d729e39073eeda5" title="set as rotation quaternion ( Построить поворотный по углам эллера) ">setRotationYawPitchRoll</a>(ea.<a class="code" href="classgbmath_1_1euler__angles.html#af37e794547bf0e12895ded562d3e692d" title="Yaw around the y-axis, in radians. ">yaw</a>, ea.<a class="code" href="classgbmath_1_1euler__angles.html#ac57fdf74e2436300b583140846581f76" title="Pitch around the x-axis, in radians. ">pitch</a>, ea.<a class="code" href="classgbmath_1_1euler__angles.html#abc5b7aa0a0bd56ce1b107bf2908392a4" title="Roll around the z-axis, in radians. ">roll</a>);</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;}</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;}</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;</div>
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